Pre-Algebra Examples

$\frac{y}{3} - \frac{y}{4} = 72$

Step 1

Rewrite in slope-intercept form.

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Step 1.1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 1.2

Simplify the left side.

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Step 1.2.1

Simplify $\frac{y}{3} - \frac{y}{4}$ .

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Step 1.2.1.1

To write $\frac{y}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{y}{3} \cdot \frac{4}{4} - \frac{y}{4} = 72$

Step 1.2.1.2

To write $- \frac{y}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{y}{3} \cdot \frac{4}{4} - \frac{y}{4} \cdot \frac{3}{3} = 72$

Step 1.2.1.3

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.2.1.3.1

Multiply $\frac{y}{3}$ by $\frac{4}{4}$ .

$\frac{y \cdot 4}{3 \cdot 4} - \frac{y}{4} \cdot \frac{3}{3} = 72$

Step 1.2.1.3.2

Multiply $3$ by $4$ .

$\frac{y \cdot 4}{12} - \frac{y}{4} \cdot \frac{3}{3} = 72$

Step 1.2.1.3.3

Multiply $\frac{y}{4}$ by $\frac{3}{3}$ .

$\frac{y \cdot 4}{12} - \frac{y \cdot 3}{4 \cdot 3} = 72$

Step 1.2.1.3.4

Multiply $4$ by $3$ .

$\frac{y \cdot 4}{12} - \frac{y \cdot 3}{12} = 72$

Step 1.2.1.4

Combine the numerators over the common denominator.

$\frac{y \cdot 4 - y \cdot 3}{12} = 72$

Step 1.2.1.5

Simplify the numerator.

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Step 1.2.1.5.1

Factor $y$ out of $y \cdot 4 - y \cdot 3$ .

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Step 1.2.1.5.1.1

Factor $y$ out of $y \cdot 4$ .

$\frac{y (4) - y \cdot 3}{12} = 72$

Step 1.2.1.5.1.2

Factor $y$ out of $- y \cdot 3$ .

$\frac{y (4) + y (- 1 \cdot 3)}{12} = 72$

Step 1.2.1.5.1.3

Factor $y$ out of $y (4) + y (- 1 \cdot 3)$ .

$\frac{y (4 - 1 \cdot 3)}{12} = 72$

Step 1.2.1.5.2

Multiply $- 1$ by $3$ .

$\frac{y (4 - 3)}{12} = 72$

Step 1.2.1.5.3

Subtract $3$ from $4$ .

$\frac{y \cdot 1}{12} = 72$

Step 1.2.1.6

Multiply $y$ by $1$ .

$\frac{y}{12} = 72$

Step 1.3

Multiply both sides of the equation by $12$ .

$12 \frac{y}{12} = 12 \cdot 72$

Step 1.4

Simplify both sides of the equation.

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Step 1.4.1

Simplify the left side.

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Step 1.4.1.1

Cancel the common factor of $12$ .

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Step 1.4.1.1.1

Cancel the common factor.

$12 \frac{y}{12} = 12 \cdot 72$

Step 1.4.1.1.2

Rewrite the expression.

$y = 12 \cdot 72$

Step 1.4.2

Simplify the right side.

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Step 1.4.2.1

Multiply $12$ by $72$ .

$y = 864$

Step 2

Using the slope-intercept form, the y-intercept is $864$ .

$b = 864$

Step 3

y-intercept in point form.

$(0, 864)$

Step 4